RESEARCH PAPER
Uncertainty propagation in structural reliability with implicit limit state functions under aleatory and epistemic uncertainties
1
School of Reliability and Systems Engineering, Beihang University, Xueyuan Road No.37, Haidian, District, Beijing 100191, China
2
Science and Technology on Reliability and Environmental Engineering Laboratory, Beihang University, Xueyuan Road No.37, Haidian District, Beijing 100191, China
3
Institute of Unmanned System, Beihang University, Xueyuan Road No.37, Haidian District, Beijing 100191, China
4
School of Aeronautic Science and Engineering, Beihang University, Xueyuan Road No.37, Haidian District, Beijing 100191, China
Publication date: 2021-06-30
Eksploatacja i Niezawodność – Maintenance and Reliability 2021;23(2):231-241
HIGHLIGHTS
- A novel surrogate model is given for implicit function under uncertain random variable.
- The concepts of chance reliability and chance reliability index (CRI) are proposed.
- A new level-2 uncertainty propagation model is provided for uncertain random structure.
- The principles for choosing reasonable uncertainty propagation types are presented.
KEYWORDS
structural reliabilityuncertainty quantificationuncertainty propagationreliability indexuncertainty theory
ABSTRACT
Uncertainty propagation plays a pivotal role in structural reliability assessment. This paper introduces a novel uncertainty propagation method for structural reliability under different knowledge stages based on probability theory, uncertainty theory and chance theory. Firstly,
a surrogate model combining the uniform design and least-squares method is presented to simulate the implicit limit state function with random and uncertain variables. Then, a novel quantification method based on chance theory is derived herein, to calculate the structural
reliability under mixed aleatory and epistemic uncertainties. The concepts of chance reliability and chance reliability index (CRI) are defined to show the reliable degree of structure. Besides, the selection principles of uncertainty propagation types and the corresponding reliability estimation methods are given according to the different knowledge stages. The proposed methods are finally applied in a practical structural reliability problem, which illustrates the effectiveness and advantages of the techniques presented in this work.
REFERENCES (40)
1.
Cremona C, Gao Y. The possibilistic reliability theory: theoretical aspects and applications. Structural Safety 1997; 19(2): 173-201, https://doi.org/10.1016/S0167-....
2.
Durga Rao K, Kushwaha HS, Verma AK, et al. Quantification of epistemic and aleatory uncertainties in level-1 probabilistic safety assessment studies. Reliability Engineering & System Safety 2007; 92(7): 947-956, https://doi.org/10.1016/j.ress....
3.
Fang K. The uniform design: application of number-theoretic methods in experimental. Acta Mathematicae Applicatae Sinica 1980; 3(4): 363-372.
4.
Fang P, Li S, Guo X, Wen Z. Response surface method based on uniform design and weighted least squares for non-probabilistic reliability analysis. International Journal for Numerical Methods in Engineering 2020; 121(18): 4050-4069, https://doi.org/10.1002/nme.64....
5.
Gao HY, Zhang XQ. Reliability-based design optimization under fuzzy and interval variables based on entropy theory. Eksploatacja i Niezawodnosc - Maintenance and Reliability 2019; 21(3): 430-439, https://doi.org/10.17531/ein.2....
6.
Guimaraes H, Matos JC, Henriques AA. An innovative adaptive sparse response surface method for structural reliability analysis. Structural Safety 2018; 73: 12-28, https://doi.org/10.1016/j.stru....
7.
Hu C, Youn BD, Wang PF. Engineering design under uncertainty and health prognostics. Springer 2019, https://doi.org/10.1007/978-3-....
8.
Hu LH, Kang R, Pan X, et al. Risk assessment of uncertain random system-Level-1 and level-2 joint propagation of uncertainty and probability in fault tree analysis. Reliability Engineering & System Safety 2020; 198: 106874, https://doi.org/10.1016/j.ress....
9.
Huang HZ. Structural reliability analysis using fuzzy sets theory. Eksploatacja i Niezawodnosc - Maintenance and Reliability 2012; 14(4):284-294.
10.
Kiureghian AD, Ditlevsen O. Aleatory or epistemic? Does it matter? Structural Safety 2009; 31(2): 105-112, https://doi.org/10.1016/j.stru....
11.
Ke H, Liu H, Tian G. An uncertain random programming model for project scheduling problem. International Journal of Intelligent Systems 2015; 30(1): 66-79, https://doi.org/10.1002/int.21....
12.
Kang R, Zhang Q, Zeng Z, Zio E, Li X. Measuring reliability under epistemic uncertainty: review on non‐probabilistic reliability metrics. Chinese Journal of Aeronautics 2016; 29(3): 571‐579, https://doi.org/10.1016/j.cja.....
13.
Li, HB, Nie, XB. Structural reliability analysis with fuzzy random variables using error principle. Engineering Applications of Artificial Intelligence 2018; 67: 91-99, https://doi.org/10.1016/j.enga....
14.
Limbourg P, Rocquigny E, Andrianov G. Accelerated uncertainty propagation in two-level probabilistic studies under monotony. Reliability Engineering & System Safety 2010; 95:998-1010, https://doi.org/10.1016/j.ress....
16.
Liu B. Why is there a need for uncertainty theory? Journal of Uncertain Systems 2012; 6(1): 3-10.
17.
Liu B. Some research problems in uncertainty theory. Journal of Uncertain System 2009; 2(1): 3-10.
19.
Liu Y, Yao K. Option pricing formulas for uncertain exponential Ornstein-Uhlenbeck model with dividends. Soft Computing 2020; 20: 1-9, https://doi.org/10.1007/s00500....
20.
Liu YH. Uncertain random variables: a mixture of uncertainty and randomness. Soft Computing 2013; 17(4): 625-634, https://doi.org/10.1007/s00500....
21.
Liu YH. Uncertain random programming with applications. Fuzzy Optimization and Decision Making 2013; 12(2): 153-169, https://doi.org/10.1007/s10700....
22.
Malakzadeh K, Daei M. Hybrid FORM-Sampling simulation method for finding design point and importance vector in structural reliability.Applied Soft Computing 2020; 92: 1-13, https://doi.org/10.1016/j.asoc....
23.
Melchers RE, Beck AT. Structural reliability analysis and prediction (3nd ed.). New York: John Wiley 2008.
24.
Nirmala K, Babu KS, Reddy KH. Design and optimization of mechanical components and its mechanism using Monte Carlo simulation. International Journal of Engineering Science 2017; 3(6): 675-680.
25.
Qin ZF. Uncertain random goal programming. Fuzzy Optimization and Decision Making 2018; 17(4): 375-386, https://doi.org/10.1007/s10700....
26.
Sohag K, Yiannis P. Applications of Bayesian networks and Petri nets in safety, reliability, and risk assessments: A review, Safety Science 2019; 115: 154-175, https://doi.org/10.1016/j.ssci....
27.
Sun B, Li MM, Liao BP, et al. Time-variant reliability modeling based on hybrid non-probability method. Archive of Applied Mechanics 2020; 90(2): 209-219, https://doi.org/10.1007/s00419....
28.
Wang ZH, Wang ZL, Yu S. Time-dependent mechanism reliability analysis based on envelope function and vine-copula function. Mechanism and Machine Theory 2019; 134: 667-684, https://doi.org/10.1016/j.mech....
29.
Wang W, Wang J, Fuj-h, Lu G-D. A moment-matching based method for the analysis of manipulator's repeatability of positioning with arbitrarily distributed joint clearances. Eksploatacja i Niezawodnosc - Maintenance and Reliability 2019; 21(1): 10-20, https://doi.org/10.17531/ein.2....
30.
Wen M, Han Q, Yang Y, et al. Uncertain optimization model for multi-echelon spare parts supply system. Applied Soft Computing 2017; 56(C): 646-654, https://doi.org/10.1016/j.asoc....
31.
Wen M, Kang R. Reliability analysis in uncertain random system. Fuzzy Optimization and Decision Making 2016; 15(4): 491-506, https://doi.org/10.1007/s10700....
32.
Yao K, Zhou J, Ruin time of uncertain insurance risk process. IEEE Transactions on Fuzzy Systems 2018; 26(1): 19-28, https://doi.org/10.1109/TFUZZ.....
33.
Zhang L, Zhang JG, Zhai H, Zhou S. A new assessment method of mechanism reliability based on chance measure under fuzzy and random uncertainties. Eksploatacja i Niezawodnosc - Maintenance and Reliability 2018; 20 (2): 219-228, https://doi.org/10.17531/ein.2....
34.
Zhang Q, Kang R, Wen M. A new method of level-2 uncertainty analysis in risk assessment based on uncertainty theory. Soft Computing 2018; 22(17): 5867-5877, https://doi.org/10.1007/s00500....
35.
Zhou S, Zhang JG, Zhang L, et al. Advanced reliability analysis method for mechanisms based on uncertain measure. Journal of Intelligent & Fuzzy Systems 2020; 39(1): 1045-1059, https://doi.org/10.3233/JIFS-1....
36.
Zhang Q. A new approximate method for uncertainty propagation in system reliability analysis. Reliability Engineering & System Safety 1990; 29(2): 261-275, https://doi.org/10.1016/0951-8....
37.
Zhang L, Zhang JG, You LF, Zhou S. Reliability analysis of structures based on a probability uncertainty hybrid model. Quality and Reliability Engineering International 2019; 35: 263-279, https://doi.org/10.1002/qre.23....
38.
Zhang Q, Kang R, Wen M. Belief reliability for uncertain random systems. IEEE Transactions on Fuzzy Systems 2018; 26(6): 3605-3614, https://doi.org/10.1109/TFUZZ.....
39.
Zhang Z, Ruan XX, Duan MF, et al. An efficient epistemic uncertainty analysis method using evidence theory. Computer Methods in Applied Mechanics and Engineering 2018; 339: 443-466, https://doi.org/10.1016/j.cma.....
40.
Zhao W, Fan F, Wang W. Non-linear partial least squares response surface method for structural reliability analysis. Reliability Engineering & System Safety 2017; 161: 69-77, https://doi.org/10.1016/j.ress....
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